[Verse 1] Take a plus b, raise it high To the power n up in the sky What unfolds is more than meets the eye A perfect pattern, here's the why Each term follows ancient law Pascal's triangle holds the awe Coefficients dancing in a row From zero k to n they go [Chorus] Binomial theorem breaks it down Sum from zero, spin around C of n choose k times a to the n minus k Times b to the k, that's the key Factorials unlock the door N factorial and so much more Divided by k times n minus k Pascal's magic, can't you see [Verse 2] Start with one, then one one Second row's where patterns run One two one, the third appears Building blocks through all the years Each number born from two above Addition's simple gift of love The triangle grows, row by row Binomial secrets start to show [Chorus] Binomial theorem breaks it down Sum from zero, spin around C of n choose k times a to the n minus k Times b to the k, that's the key Factorials unlock the door N factorial and so much more Divided by k times n minus k Pascal's magic, can't you see [Bridge] Combinations tell the tale How many ways will never fail To choose k objects from the whole N factorial plays its role Algebra meets counting games Probability shares the same One formula, three worlds collide Mathematical joy we can't hide [Chorus] Binomial theorem breaks it down Sum from zero, spin around C of n choose k times a to the n minus k Times b to the k, that's the key Factorials unlock the door N factorial and so much more Divided by k times n minus k Pascal's magic, can't you see [Outro] Simple binomial explodes with grace Into n plus one terms taking place The blueprint's drawn in triangle form Beauty born from algebraic storm
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